ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <iostream>
  24 #include <vector>
  25 #include <stdexcept>
  26
  27 #include "mul.h"
  28 #include "add.h"
  29 #include "power.h"
  30 #include "matrix.h"
  31 #include "archive.h"
  32 #include "utils.h"
  33
  34 namespace GiNaC {
  35
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  37
  38 //////////
  39 // default ctor, dtor, copy ctor, assignment operator and helpers
  40 //////////
  41
  42 mul::mul()
  43 {
  44         tinfo_key = TINFO_mul;
  45 }
  46
  47 DEFAULT_COPY(mul)
  48 DEFAULT_DESTROY(mul)
  49
  50 //////////
  51 // other ctors
  52 //////////
  53
  54 // public
  55
  56 mul::mul(const ex & lh, const ex & rh)
  57 {
  58         tinfo_key = TINFO_mul;
  59         overall_coeff = _ex1;
  60         construct_from_2_ex(lh,rh);
  61         GINAC_ASSERT(is_canonical());
  62 }
  63
  64 mul::mul(const exvector & v)
  65 {
  66         tinfo_key = TINFO_mul;
  67         overall_coeff = _ex1;
  68         construct_from_exvector(v);
  69         GINAC_ASSERT(is_canonical());
  70 }
  71
  72 mul::mul(const epvector & v)
  73 {
  74         tinfo_key = TINFO_mul;
  75         overall_coeff = _ex1;
  76         construct_from_epvector(v);
  77         GINAC_ASSERT(is_canonical());
  78 }
  79
  80 mul::mul(const epvector & v, const ex & oc)
  81 {
  82         tinfo_key = TINFO_mul;
  83         overall_coeff = oc;
  84         construct_from_epvector(v);
  85         GINAC_ASSERT(is_canonical());
  86 }
  87
  88 mul::mul(epvector * vp, const ex & oc)
  89 {
  90         tinfo_key = TINFO_mul;
  91         GINAC_ASSERT(vp!=0);
  92         overall_coeff = oc;
  93         construct_from_epvector(*vp);
  94         delete vp;
  95         GINAC_ASSERT(is_canonical());
  96 }
  97
  98 mul::mul(const ex & lh, const ex & mh, const ex & rh)
  99 {
 100         tinfo_key = TINFO_mul;
 101         exvector factors;
 102         factors.reserve(3);
 103         factors.push_back(lh);
 104         factors.push_back(mh);
 105         factors.push_back(rh);
 106         overall_coeff = _ex1;
 107         construct_from_exvector(factors);
 108         GINAC_ASSERT(is_canonical());
 109 }
 110
 111 //////////
 112 // archiving
 113 //////////
 114
 115 DEFAULT_ARCHIVING(mul)
 116
 117 //////////
 118 // functions overriding virtual functions from base classes
 119 //////////
 120
 121 // public
 122
 123 void mul::print(const print_context & c, unsigned level) const
 124 {
 125         if (is_a<print_tree>(c)) {
 126
 127                 inherited::print(c, level);
 128
 129         } else if (is_a<print_csrc>(c)) {
 130
 131                 if (precedence() <= level)
 132                         c.s << "(";
 133
 134                 if (!overall_coeff.is_equal(_ex1)) {
 135                         overall_coeff.print(c, precedence());
 136                         c.s << "*";
 137                 }
 138
 139                 // Print arguments, separated by "*" or "/"
 140                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 141                 while (it != itend) {
 142
 143                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 144                         if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) {
 145                                 if (is_a<print_csrc_cl_N>(c))
 146                                         c.s << "recip(";
 147                                 else
 148                                         c.s << "1.0/";
 149                         }
 150
 151                         // If the exponent is 1 or -1, it is left out
 152                         if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0)
 153                                 it->rest.print(c, precedence());
 154                         else {
 155                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 156                                 (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
 157                         }
 158
 159                         // Separator is "/" for negative integer powers, "*" otherwise
 160                         ++it;
 161                         if (it != itend) {
 162                                 if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
 163                                         c.s << "/";
 164                                 else
 165                                         c.s << "*";
 166                         }
 167                 }
 168
 169                 if (precedence() <= level)
 170                         c.s << ")";
 171
 172         } else if (is_a<print_python_repr>(c)) {
 173                 c.s << class_name() << '(';
 174                 unsigned end = nops();
 175                 if (end)
 176                         op(0).print(c);
 177                 for (unsigned i=1; i<end; ++i) {
 178                         c.s << ',';
 179                         op(i).print(c);
 180                 }
 181                 c.s << ')';
 182         } else {
 183
 184                 if (precedence() <= level) {
 185                         if (is_a<print_latex>(c))
 186                                 c.s << "{(";
 187                         else
 188                                 c.s << "(";
 189                 }
 190
 191                 bool first = true;
 192
 193                 // First print the overall numeric coefficient
 194                 numeric coeff = ex_to<numeric>(overall_coeff);
 195                 if (coeff.csgn() == -1)
 196                         c.s << '-';
 197                 if (!coeff.is_equal(_num1) &&
 198                         !coeff.is_equal(_num_1)) {
 199                         if (coeff.is_rational()) {
 200                                 if (coeff.is_negative())
 201                                         (-coeff).print(c);
 202                                 else
 203                                         coeff.print(c);
 204                         } else {
 205                                 if (coeff.csgn() == -1)
 206                                         (-coeff).print(c, precedence());
 207                                 else
 208                                         coeff.print(c, precedence());
 209                         }
 210                         if (is_a<print_latex>(c))
 211                                 c.s << ' ';
 212                         else
 213                                 c.s << '*';
 214                 }
 215
 216                 // Then proceed with the remaining factors
 217                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 218                 while (it != itend) {
 219                         if (!first) {
 220                                 if (is_a<print_latex>(c))
 221                                         c.s << ' ';
 222                                 else
 223                                         c.s << '*';
 224                         } else {
 225                                 first = false;
 226                         }
 227                         recombine_pair_to_ex(*it).print(c, precedence());
 228                         ++it;
 229                 }
 230
 231                 if (precedence() <= level) {
 232                         if (is_a<print_latex>(c))
 233                                 c.s << ")}";
 234                         else
 235                                 c.s << ")";
 236                 }
 237         }
 238 }
 239
 240 bool mul::info(unsigned inf) const
 241 {
 242         switch (inf) {
 243                 case info_flags::polynomial:
 244                 case info_flags::integer_polynomial:
 245                 case info_flags::cinteger_polynomial:
 246                 case info_flags::rational_polynomial:
 247                 case info_flags::crational_polynomial:
 248                 case info_flags::rational_function: {
 249                         epvector::const_iterator i = seq.begin(), end = seq.end();
 250                         while (i != end) {
 251                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 252                                         return false;
 253                                 ++i;
 254                         }
 255                         return overall_coeff.info(inf);
 256                 }
 257                 case info_flags::algebraic: {
 258                         epvector::const_iterator i = seq.begin(), end = seq.end();
 259                         while (i != end) {
 260                                 if ((recombine_pair_to_ex(*i).info(inf)))
 261                                         return true;
 262                                 ++i;
 263                         }
 264                         return false;
 265                 }
 266         }
 267         return inherited::info(inf);
 268 }
 269
 270 int mul::degree(const ex & s) const
 271 {
 272         // Sum up degrees of factors
 273         int deg_sum = 0;
 274         epvector::const_iterator i = seq.begin(), end = seq.end();
 275         while (i != end) {
 276                 if (ex_to<numeric>(i->coeff).is_integer())
 277                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 278                 ++i;
 279         }
 280         return deg_sum;
 281 }
 282
 283 int mul::ldegree(const ex & s) const
 284 {
 285         // Sum up degrees of factors
 286         int deg_sum = 0;
 287         epvector::const_iterator i = seq.begin(), end = seq.end();
 288         while (i != end) {
 289                 if (ex_to<numeric>(i->coeff).is_integer())
 290                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 291                 ++i;
 292         }
 293         return deg_sum;
 294 }
 295
 296 ex mul::coeff(const ex & s, int n) const
 297 {
 298         exvector coeffseq;
 299         coeffseq.reserve(seq.size()+1);
 300
 301         if (n==0) {
 302                 // product of individual coeffs
 303                 // if a non-zero power of s is found, the resulting product will be 0
 304                 epvector::const_iterator i = seq.begin(), end = seq.end();
 305                 while (i != end) {
 306                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 307                         ++i;
 308                 }
 309                 coeffseq.push_back(overall_coeff);
 310                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 311         }
 312
 313         epvector::const_iterator i = seq.begin(), end = seq.end();
 314         bool coeff_found = false;
 315         while (i != end) {
 316                 ex t = recombine_pair_to_ex(*i);
 317                 ex c = t.coeff(s, n);
 318                 if (!c.is_zero()) {
 319                         coeffseq.push_back(c);
 320                         coeff_found = 1;
 321                 } else {
 322                         coeffseq.push_back(t);
 323                 }
 324                 ++i;
 325         }
 326         if (coeff_found) {
 327                 coeffseq.push_back(overall_coeff);
 328                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 329         }
 330
 331         return _ex0;
 332 }
 333
 334 /** Perform automatic term rewriting rules in this class.  In the following
 335  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 336  *  stand for such expressions that contain a plain number.
 337  *  - *(...,x;0) -> 0
 338  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 339  *  - *(x;1) -> x
 340  *  - *(;c) -> c
 341  *
 342  *  @param level cut-off in recursive evaluation */
 343 ex mul::eval(int level) const
 344 {
 345         epvector *evaled_seqp = evalchildren(level);
 346         if (evaled_seqp) {
 347                 // do more evaluation later
 348                 return (new mul(evaled_seqp,overall_coeff))->
 349                            setflag(status_flags::dynallocated);
 350         }
 351
 352 #ifdef DO_GINAC_ASSERT
 353         epvector::const_iterator i = seq.begin(), end = seq.end();
 354         while (i != end) {
 355                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 356                              (!(ex_to<numeric>(i->coeff).is_integer())));
 357                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 358                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 359                     print(print_tree(std::cerr));
 360                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 361                 /* for paranoia */
 362                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 363                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 364                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 365                 /* end paranoia */
 366                 ++i;
 367         }
 368 #endif // def DO_GINAC_ASSERT
 369
 370         if (flags & status_flags::evaluated) {
 371                 GINAC_ASSERT(seq.size()>0);
 372                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 373                 return *this;
 374         }
 375
 376         int seq_size = seq.size();
 377         if (overall_coeff.is_zero()) {
 378                 // *(...,x;0) -> 0
 379                 return _ex0;
 380         } else if (seq_size==0) {
 381                 // *(;c) -> c
 382                 return overall_coeff;
 383         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 384                 // *(x;1) -> x
 385                 return recombine_pair_to_ex(*(seq.begin()));
 386         } else if ((seq_size==1) &&
 387                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 388                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 389                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 390                 const add & addref = ex_to<add>((*seq.begin()).rest);
 391                 epvector *distrseq = new epvector();
 392                 distrseq->reserve(addref.seq.size());
 393                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 394                 while (i != end) {
 395                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 396                         ++i;
 397                 }
 398                 return (new add(distrseq,
 399                                 ex_to<numeric>(addref.overall_coeff).
 400                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 401                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 402         }
 403         return this->hold();
 404 }
 405
 406 ex mul::evalf(int level) const
 407 {
 408         if (level==1)
 409                 return mul(seq,overall_coeff);
 410
 411         if (level==-max_recursion_level)
 412                 throw(std::runtime_error("max recursion level reached"));
 413
 414         epvector *s = new epvector();
 415         s->reserve(seq.size());
 416
 417         --level;
 418         epvector::const_iterator i = seq.begin(), end = seq.end();
 419         while (i != end) {
 420                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 421                                                            i->coeff));
 422                 ++i;
 423         }
 424         return mul(s, overall_coeff.evalf(level));
 425 }
 426
 427 ex mul::evalm(void) const
 428 {
 429         // numeric*matrix
 430         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 431          && is_ex_of_type(seq[0].rest, matrix))
 432                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 433
 434         // Evaluate children first, look whether there are any matrices at all
 435         // (there can be either no matrices or one matrix; if there were more
 436         // than one matrix, it would be a non-commutative product)
 437         epvector *s = new epvector;
 438         s->reserve(seq.size());
 439
 440         bool have_matrix = false;
 441         epvector::iterator the_matrix;
 442
 443         epvector::const_iterator i = seq.begin(), end = seq.end();
 444         while (i != end) {
 445                 const ex &m = recombine_pair_to_ex(*i).evalm();
 446                 s->push_back(split_ex_to_pair(m));
 447                 if (is_ex_of_type(m, matrix)) {
 448                         have_matrix = true;
 449                         the_matrix = s->end() - 1;
 450                 }
 451                 ++i;
 452         }
 453
 454         if (have_matrix) {
 455
 456                 // The product contained a matrix. We will multiply all other factors
 457                 // into that matrix.
 458                 matrix m = ex_to<matrix>(the_matrix->rest);
 459                 s->erase(the_matrix);
 460                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 461                 return m.mul_scalar(scalar);
 462
 463         } else
 464                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 465 }
 466
 467 ex mul::simplify_ncmul(const exvector & v) const
 468 {
 469         if (seq.empty())
 470                 return inherited::simplify_ncmul(v);
 471
 472         // Find first noncommutative element and call its simplify_ncmul()
 473         epvector::const_iterator i = seq.begin(), end = seq.end();
 474         while (i != end) {
 475                 if (i->rest.return_type() == return_types::noncommutative)
 476                         return i->rest.simplify_ncmul(v);
 477                 ++i;
 478         }
 479         return inherited::simplify_ncmul(v);
 480 }
 481
 482 // protected
 483
 484 /** Implementation of ex::diff() for a product.  It applies the product rule.
 485  *  @see ex::diff */
 486 ex mul::derivative(const symbol & s) const
 487 {
 488         unsigned num = seq.size();
 489         exvector addseq;
 490         addseq.reserve(num);
 491
 492         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 493         epvector mulseq = seq;
 494         epvector::const_iterator i = seq.begin(), end = seq.end();
 495         epvector::iterator i2 = mulseq.begin();
 496         while (i != end) {
 497                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 498                                              i->rest.diff(s));
 499                 ep.swap(*i2);
 500                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 501                 ep.swap(*i2);
 502                 ++i; ++i2;
 503         }
 504         return (new add(addseq))->setflag(status_flags::dynallocated);
 505 }
 506
 507 int mul::compare_same_type(const basic & other) const
 508 {
 509         return inherited::compare_same_type(other);
 510 }
 511
 512 bool mul::is_equal_same_type(const basic & other) const
 513 {
 514         return inherited::is_equal_same_type(other);
 515 }
 516
 517 unsigned mul::return_type(void) const
 518 {
 519         if (seq.empty()) {
 520                 // mul without factors: should not happen, but commutes
 521                 return return_types::commutative;
 522         }
 523
 524         bool all_commutative = true;
 525         epvector::const_iterator noncommutative_element; // point to first found nc element
 526
 527         epvector::const_iterator i = seq.begin(), end = seq.end();
 528         while (i != end) {
 529                 unsigned rt = i->rest.return_type();
 530                 if (rt == return_types::noncommutative_composite)
 531                         return rt; // one ncc -> mul also ncc
 532                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 533                         // first nc element found, remember position
 534                         noncommutative_element = i;
 535                         all_commutative = false;
 536                 }
 537                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 538                         // another nc element found, compare type_infos
 539                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 540                                 // diffent types -> mul is ncc
 541                                 return return_types::noncommutative_composite;
 542                         }
 543                 }
 544                 ++i;
 545         }
 546         // all factors checked
 547         return all_commutative ? return_types::commutative : return_types::noncommutative;
 548 }
 549
 550 unsigned mul::return_type_tinfo(void) const
 551 {
 552         if (seq.empty())
 553                 return tinfo_key;  // mul without factors: should not happen
 554
 555         // return type_info of first noncommutative element
 556         epvector::const_iterator i = seq.begin(), end = seq.end();
 557         while (i != end) {
 558                 if (i->rest.return_type() == return_types::noncommutative)
 559                         return i->rest.return_type_tinfo();
 560                 ++i;
 561         }
 562         // no noncommutative element found, should not happen
 563         return tinfo_key;
 564 }
 565
 566 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 567 {
 568         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 569 }
 570
 571 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 572 {
 573         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 574 }
 575
 576 expair mul::split_ex_to_pair(const ex & e) const
 577 {
 578         if (is_ex_exactly_of_type(e,power)) {
 579                 const power & powerref = ex_to<power>(e);
 580                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 581                         return expair(powerref.basis,powerref.exponent);
 582         }
 583         return expair(e,_ex1);
 584 }
 585
 586 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 587                                           const ex & c) const
 588 {
 589         // to avoid duplication of power simplification rules,
 590         // we create a temporary power object
 591         // otherwise it would be hard to correctly simplify
 592         // expression like (4^(1/3))^(3/2)
 593         if (are_ex_trivially_equal(c,_ex1))
 594                 return split_ex_to_pair(e);
 595
 596         return split_ex_to_pair(power(e,c));
 597 }
 598
 599 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 600                                             const ex & c) const
 601 {
 602         // to avoid duplication of power simplification rules,
 603         // we create a temporary power object
 604         // otherwise it would be hard to correctly simplify
 605         // expression like (4^(1/3))^(3/2)
 606         if (are_ex_trivially_equal(c,_ex1))
 607                 return p;
 608
 609         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 610 }
 611
 612 ex mul::recombine_pair_to_ex(const expair & p) const
 613 {
 614         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 615                 return p.rest;
 616         else
 617                 return power(p.rest,p.coeff);
 618 }
 619
 620 bool mul::expair_needs_further_processing(epp it)
 621 {
 622         if (is_ex_exactly_of_type((*it).rest,mul) &&
 623                 ex_to<numeric>((*it).coeff).is_integer()) {
 624                 // combined pair is product with integer power -> expand it
 625                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 626                 return true;
 627         }
 628         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 629                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 630                 if (!ep.is_equal(*it)) {
 631                         // combined pair is a numeric power which can be simplified
 632                         *it = ep;
 633                         return true;
 634                 }
 635                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 636                         // combined pair has coeff 1 and must be moved to the end
 637                         return true;
 638                 }
 639         }
 640         return false;
 641 }
 642
 643 ex mul::default_overall_coeff(void) const
 644 {
 645         return _ex1;
 646 }
 647
 648 void mul::combine_overall_coeff(const ex & c)
 649 {
 650         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 651         GINAC_ASSERT(is_exactly_a<numeric>(c));
 652         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 653 }
 654
 655 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 656 {
 657         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 658         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 659         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 660         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 661 }
 662
 663 bool mul::can_make_flat(const expair & p) const
 664 {
 665         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 666         // this assertion will probably fail somewhere
 667         // it would require a more careful make_flat, obeying the power laws
 668         // probably should return true only if p.coeff is integer
 669         return ex_to<numeric>(p.coeff).is_equal(_num1);
 670 }
 671
 672 ex mul::expand(unsigned options) const
 673 {
 674         // First, expand the children
 675         epvector * expanded_seqp = expandchildren(options);
 676         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 677
 678         // Now, look for all the factors that are sums and multiply each one out
 679         // with the next one that is found while collecting the factors which are
 680         // not sums
 681         int number_of_adds = 0;
 682         ex last_expanded = _ex1;
 683         epvector non_adds;
 684         non_adds.reserve(expanded_seq.size());
 685         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 686         while (cit != last) {
 687                 if (is_ex_exactly_of_type(cit->rest, add) &&
 688                         (cit->coeff.is_equal(_ex1))) {
 689                         ++number_of_adds;
 690                         if (is_ex_exactly_of_type(last_expanded, add)) {
 691                                 const add & add1 = ex_to<add>(last_expanded);
 692                                 const add & add2 = ex_to<add>(cit->rest);
 693                                 int n1 = add1.nops();
 694                                 int n2 = add2.nops();
 695                                 exvector distrseq;
 696                                 distrseq.reserve(n1*n2);
 697                                 for (int i1=0; i1<n1; ++i1) {
 698                                         for (int i2=0; i2<n2; ++i2) {
 699                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 700                                         }
 701                                 }
 702                                 last_expanded = (new add(distrseq))->
 703                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 704                         } else {
 705                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 706                                 last_expanded = cit->rest;
 707                         }
 708                 } else {
 709                         non_adds.push_back(*cit);
 710                 }
 711                 ++cit;
 712         }
 713         if (expanded_seqp)
 714                 delete expanded_seqp;
 715
 716         // Now the only remaining thing to do is to multiply the factors which
 717         // were not sums into the "last_expanded" sum
 718         if (is_ex_exactly_of_type(last_expanded, add)) {
 719                 const add & finaladd = ex_to<add>(last_expanded);
 720                 exvector distrseq;
 721                 int n = finaladd.nops();
 722                 distrseq.reserve(n);
 723                 for (int i=0; i<n; ++i) {
 724                         epvector factors = non_adds;
 725                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 726                         distrseq.push_back((new mul(factors, overall_coeff))->
 727                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 728                 }
 729                 return ((new add(distrseq))->
 730                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 731         }
 732         non_adds.push_back(split_ex_to_pair(last_expanded));
 733         return (new mul(non_adds, overall_coeff))->
 734                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 735 }
 736
 737
 738 //////////
 739 // new virtual functions which can be overridden by derived classes
 740 //////////
 741
 742 // none
 743
 744 //////////
 745 // non-virtual functions in this class
 746 //////////
 747
 748
 749 /** Member-wise expand the expairs representing this sequence.  This must be
 750  *  overridden from expairseq::expandchildren() and done iteratively in order
 751  *  to allow for early cancallations and thus safe memory.
 752  *
 753  *  @see mul::expand()
 754  *  @return pointer to epvector containing expanded representation or zero
 755  *  pointer, if sequence is unchanged. */
 756 epvector * mul::expandchildren(unsigned options) const
 757 {
 758         const epvector::const_iterator last = seq.end();
 759         epvector::const_iterator cit = seq.begin();
 760         while (cit!=last) {
 761                 const ex & factor = recombine_pair_to_ex(*cit);
 762                 const ex & expanded_factor = factor.expand(options);
 763                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 764
 765                         // something changed, copy seq, eval and return it
 766                         epvector *s = new epvector;
 767                         s->reserve(seq.size());
 768
 769                         // copy parts of seq which are known not to have changed
 770                         epvector::const_iterator cit2 = seq.begin();
 771                         while (cit2!=cit) {
 772                                 s->push_back(*cit2);
 773                                 ++cit2;
 774                         }
 775                         // copy first changed element
 776                         s->push_back(split_ex_to_pair(expanded_factor));
 777                         ++cit2;
 778                         // copy rest
 779                         while (cit2!=last) {
 780                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 781                                 ++cit2;
 782                         }
 783                         return s;
 784                 }
 785                 ++cit;
 786         }
 787
 788         return 0; // nothing has changed
 789 }
 790
 791 } // namespace GiNaC